dnorm(0, mean = 0, sd = 1)

[1] 0.3989423

dnorm(0, mean = 0, sd = 1)

[1] 0.3989423

1/sqrt(2*pi)

[1] 0.3989423

pnorm(1.23)

[1] 0.8906514

qnorm(.7642)

[1] 0.7198782

(x <- rnorm(50, 3.5, 2))

 [1] 2.33448392 2.77918492 3.42299643 2.31131660 2.60653563 0.02763644
 [7] 3.55064888 6.85664402 5.82705124 3.64368520 4.50130431 1.46029144
[13] 6.99153101 4.04737999 2.50895239 4.36117090 4.37842959 6.83909902
[19] 3.84238174 4.29535268 2.80893234 4.63916527 2.84863341 2.90743985
[25] 7.22012745 4.38141220 1.98005164 2.77908621 1.71398360 2.48934324
[31] 6.93354143 2.01294352 2.53200680 0.16789140 1.82119098 3.13685892
[37] 4.65971326 4.24524949 0.29974642 1.60221963 2.12757168 7.53808683
[43] 4.53491946 1.96643011 5.69834018 7.09615017 7.08423452 6.08772508
[49] 4.89799893 5.95301586

hist(x)

y <- rnorm(5000, 3.5, 2)

y <- rnorm(5000, 3.5, 2)

hist(y)

dbinom(2, 5, .5)

[1] 0.3125

dbinom(2, 5, .5)

[1] 0.3125

dbinom(2, 5, .5)

[1] 0.3125

pbinom(1, 5, .3)

[1] 0.52822

dbinom(2, 5, .5)

[1] 0.3125

pbinom(1, 5, .3)

[1] 0.52822

pbinom(1, 5, .3, lower.tail = FALSE)

[1] 0.47178

dbinom(2, 5, .5)

[1] 0.3125

pbinom(1, 5, .3)

[1] 0.52822

pbinom(1, 5, .3, lower.tail = FALSE)

[1] 0.47178

pbinom(1, 5, .3) +
pbinom(1, 5, .3, lower.tail = FALSE)

[1] 1

qbinom(.163, 5, .7)

[1] 2

qbinom(.163, 5, .7)

[1] 2

rbinom(50, 10, .5)

 [1] 3 6 4 3 5 5 3 6 5 5 5 5 2 5 4 6 6 5 4 6 0 6 7 4 7 5 7 7 8 5 7 6 9 5 6
[36] 2 5 6 4 1 5 6 5 6 3 3 6 5 6 4